Make the dough: Position a rack in the lower third of the oven and preheat to 500 degrees F. Put 1/2 cup flour, the yeast and sugar in a food processor and pulse to combine. With the motor running, add 3/4 cup hot tap water (about 115 degrees F). Turn off the motor and add the cornmeal, cheese, olive oil, 1 teaspoon salt and the remaining 1 cup flour. Pulse until the dough forms a ball, then continue pulsing until smooth but still wet, about 15 more times.
Make the pizzettes: Line 2 baking sheets with parchment paper. Turn the dough out onto a lightly floured surface and knead until soft and elastic, 12 to 15 times, dusting lightly with flour if too wet to handle. Using a floured rolling pin, roll out the dough into a 1/4-inch-thick disk, about 14 inches across. Using a 3-inch-round cutter, cut the dough into 16 rounds, gathering and rerolling the scraps if needed. Transfer the rounds to the prepared pans.
Mix the olive oil, oregano, and salt and pepper to taste. Brush each round lightly with the herb oil, then top each with a slice of soppressata and 2 to 3 tomato slices. Sprinkle with the parmesan. Bake one sheet at a time, until the crusts are golden, about 8 minutes.
Drizzle the pizzettes with olive oil, season with salt and pepper, and top with the basil leaves. Serve warm or at room temperature.